Trigonometry (10th Edition)

Published by Pearson
ISBN 10: 0321671775
ISBN 13: 978-0-32167-177-6

Chapter 2 - Acute Angles and Right Triangles - Section 2.1 Trigonometric Functions of Acute Angles - 2.1 Exercises: 37

Answer

$\theta$ = 35$^{\circ}$

Work Step by Step

$\sin$($\theta$ - 20$^{\circ}$) = $\cos$(2$\theta$ + 5$^{\circ}$) $\sin$ and $\cos$ are cofunctions if the sum of the angles is 90$^{\circ}$ Therefore: ($\theta$ - 20$^{\circ}$) + (2$\theta$ + 5$^{\circ}$) = 90$^{\circ}$ 3$\theta$ - 15$^{\circ}$ = 90$^{\circ}$ 3$\theta$ = 105$^{\circ}$ $\theta$ = 35$^{\circ}$
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